text: As early as 1886, Robert von Helmholtz (son of the German physicist Hermann von Helmholtz) had observed that finely dispersed liquids have a higher vapor pressure.  By 1906, the German physical chemist Friedrich Wilhelm Küster (1861–1917) had predicted that since the vapor pressure of a finely pulverized volatile solid is greater than the vapor pressure of the bulk solid, then the melting point of the fine powder should be lower than that of the bulk solid.  Investigators such as the Russian physical chemists Pavel Nikolaevich Pavlov (or Pawlow (in German), 1872–1953) and Peter Petrovich von Weymarn (1879–1935), among others, searched for and eventually observed such melting point depression. By 1932, Czech investigator Paul Kubelka (1900–1956) had observed that the melting point of iodine in activated charcoal is depressed as much as 100 °C.  Investigators recognized that the melting point depression occurred when the change in surface energy was significant compared to the latent heat of the phase transition, which condition obtained in the case of very small particles.
  Neither Josiah Willard Gibbs nor William Thomson (Lord Kelvin) derived the Gibbs–Thomson equation.  Also, although many sources claim that British physicist J. J. Thomson derived the Gibbs–Thomson equation in 1888, he did not.  Early in the 20th century, investigators derived precursors of the Gibbs–Thomson equation.  However, in 1920, the Gibbs–Thomson equation was first derived in its modern form by two researchers working independently:  Friedrich Meissner, a student of the Estonian-German physical chemist Gustav Tammann, and Ernst Rie (1896–1921), an Austrian physicist at the University of Vienna.  These early investigators did not call the relation the "Gibbs–Thomson" equation.  That name was in use by 1910 or earlier; it originally referred to equations concerning the adsorption of solutes by interfaces between two phases — equations that Gibbs and then J. J. Thomson derived.  Hence, in the name "Gibbs–Thomson" equation, "Thomson" refers to J. J. Thomson, not William Thomson (Lord Kelvin).
  In 1871, William Thomson published an equation describing capillary action and relating the curvature of a liquid-vapor interface to the vapor pressure:
  where:
  *   =  vapor pressure at a curved interface of radius 
  *   =  vapor pressure at a flat interface () = 
  *   =  surface tension
  *   = density of vapor
  *  = density of liquid
  * ,  = radii of curvature along the principal sections of the curved interface.
  In his dissertation of 1885, Robert von Helmholtz (son of German physicist Hermann von Helmholtz) showed how the Ostwald–Freundlich equation
  could be derived from Kelvin's equation.  The Gibbs–Thomson equation can then be derived from the Ostwald–Freundlich equation via a simple substitution using the integrated form of the Clausius–Clapeyron relation:
  The Gibbs–Thomson equation can also be derived directly from Gibbs' equation for the energy of an interface between phases.
  It should be mentioned that in the literature, there is still not agreement about the specific equation to which the name "Gibbs–Thomson equation" refers.  For example, in the case of some authors, its another name for the "Ostwald–Freundlich equation"—which, in turn, is often called the "Kelvin equation"—whereas in the case of other authors, the "Gibbs–Thomson relation" is the Gibbs free energy thats required to expand the interface, and so forth.